Problem: Simplify the following expression and state the condition under which the simplification is valid. $k = \dfrac{x^2 - 4}{x - 2}$
Solution: First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = x$ $ b = \sqrt{4} = -2$ So we can rewrite the expression as: $k = \dfrac{({x} {-2})({x} + {2})} {x - 2} $ We can divide the numerator and denominator by $(x - 2)$ on condition that $x \neq 2$ Therefore $k = x + 2; x \neq 2$